A long, vertical wire carrying a current of 10A in the upward direction is placed in a region where a horizontal magnetic field of magnitude `2.0xx10^-3T` exist from south to north. Find the point where the resultant magnetic field is zero.

Explanation

Given, `vecB=2xx10^-3T`
Now, direction of `vecB` due to the
wire is `odot` in the left half and `ox`
in the right half.
`:. B_("net")=0` in the left half only
`|B_(wire)|=|vecB|` in the zy plane
`(mu_0 10)/(2pir)=2xx10^-3T`
`r=(4xx10^-7xx5)/(pixx2xx10^-3)=10^-3m`
Thus, magnetic field is zero at `r=1mm` to the left of the wire in
the indicated yz-plane.